Clean the mushrooms by wiping the loose dirt off with a towel. Cut mushrooms in half and then into slices of desired thickness (I like 1/8 inch). Heat 1 Tbls butter in a pan, add olive oil. When the pan is hot, add the green onions and start adding the mushrooms. Add them such that they never pile up more than 1/2 inch thick. If you add them all at once, they tend to pile up and steam themselves. You want them to cook by being sauteed in the butter, so add them in a metered fashion so they don't all pile up. They will shrink as they cook making room for more. You want to cook them until they start to brown around the edges. Add salt and pepper. Once they've shrunk down and become soft, add some white wine. The liquid will boil off very quickly (1-2 minutes). Add the stock and let it boil for a few minutes to condense, then add the cream and mix together into a nice sauce.

The sauce can be made thinner and more brothy and creamy by adding more stock and cream. You'll have to adjust it to the consistency and volume that you like.